Why did the butler see fit to mention to mention the king's anger?
Oznayim la'Torah: It seems that punishments were meted out, not according to the crime but according to the mood of the king or the prince. 1
Refer to 41:10:152:3 and 41:10:152:4.
Oznayim la'Torah: Hence the Torah attributed their punishment to Pharaoh's anger (40:2); and Yosef's punishment to Potifar's anger (39:19).
How could he be so brazen to address Pharaoh by name?
Rashbam: He didn't! 'Pharaoh' in Egyptian is synonymous with 'king.' 1
Rashbam: Similarly, every king of Pelishtim is called 'Avimelech;' of Yerushalayim 'Malki-Tzedek' or 'Adoni-Tzedek;' and of Amalek 'Agag.'
Why did he say "me" twice?
Rosh, Da'as Zekenim, Hadar Zekenim: He needed to show that he and the baker were equally incarcerated. If the butler had better conditions, 1 Yosef could infer that the butler would be returned and the baker killed, even without prophetic ability to interpret! 2
Refer to 41:10:152.
He should have said, 'he put us in jail.' Why did he say 'me... [and the baker]'?
Moshav Zekenim: Also nowadays the custom is, when mentioning a living and dead person, to separate them. 1
Oznayim la'Torah: He presented himself as the main sinner, minimizing the sin of the baker. 2
Malbim (to 41:9): He was proving that Yosef interpreted via Ru'ach Elokim, and not by estimation. I was the real sinner, 3 and I deserved to be punished; amidst anger at me, also Sar ha'Ofim was incarcerated. Even so, Yosef said that I will be returned to my post, and Sar ha'Ofim will be killed!
Ha'amek Davar based on Lekach Tov: I was the main sinner, and Sar ha'Ofim was secondary. Even though the primary anger was at me, it was changed through his interpretation.
Nowadays, people say "v'Yibadel l'Chayim" (PF).
Oznayim la'Torah: As the old saying goes - 'about a dead person one either speaks good, or not at all.'
Refer to 40:1:152:2 and 40:2:151:1.